Promoted Tweets will, in essence, promote what an advertiser wants when a user searches for a particular term. It will permit advertisers to insert themselves into the real-time conversation on Twitter, something they've had difficulty doing to date.
Twitter promises no irrelevant Tweets will make their way to you, even though it plans in its next phase of development to send Tweets you didn't subscribe to or search for. That will prove highly controversial because Twitter has conditioned users to not receive unwanted information.
To mitigate possible negative response it has created a relevance criteria that will gauge the effectiveness of messages --- how often they were read, replied shared and so on.
Everyone had to know that, sooner or later, the party would end. Twitter is trying to find a way to send people along relatively happy.